In this work, we consider a real scalar field surrounding a Kerr BH. It has been shown in Ref. [1]} that the backreaction of the scalar condensate is negligible because of its low energy density. It is also qualified to ignore self-interaction for the same reason. These contributions may be taken into account with the perturbation method if high-precision results are needed, which is beyond the scope of this work. Here we consider a free real scalar field on the Kerr metric,
\(\left(\nabla ^{\mu }\nabla _{\mu }+\mu ^{2}\right)\Phi =0,\) 
